Explicit Solution of the Focus Locus Problem for the Harmonic Oscillator Orbits in the Plane
- 1 January 2022
- journal article
- research article
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Journal of Geometry and Symmetry in Physics
- Vol. 64, 29-37
- https://doi.org/10.7546/jgsp-64-2022-29-37
Abstract
Dynamical orbits of the harmonic oscillator potential in the plane are ellipses which depend on a real parameter. Some time ago in this journal it has been proven by purely geometrical methods that the locus of the focuses of these ellipses are Cassinian ovals.Here we present several explicit analytic parameterizations of these remarkable curves. Nominally, their forms depend on the magnitude of the initial distance from the center of attraction and the magnitude of the initial velocity. We have found a few parameterizations in which the roles of the size and shapes can be clearly distinguished.Keywords
This publication has 6 references indexed in Scilit:
- Analytical Descriptions of Perseus SpiricsJournal of Geometry and Symmetry in Physics, 2022
- The Spiric Sections of Perseus and the Uniform Parameterizations of the Cassinian OvalsJournal of Geometry and Symmetry in Physics, 2020
- The Rectifications of the Cassinian Ovals: Third RoundJournal of Geometry and Symmetry in Physics, 2020
- Cassini Ovals in Harmonic Motion OrbitsJournal of Geometry and Symmetry in Physics, 2018
- On Some Deformations of the Cassinian OvalAIP Conference Proceedings, 2011
- Safe domain and elementary geometryEuropean Journal of Physics, 2004